There are 30 senators in a senate. For each pair of senators, the two senators are either friends of each other or enemies of each other. Every senator has exactly six enemies. Every three senators form a committee. Find the total number of committees whose members are either all friends or all enemies of each other.
So far I have reached to this solution:
1) There are total 30C2 pairs. = 435
2) If every senator has 6 enemies then 30 senators will have total 30*60/2 enemies pairs (removing double counted ) = 90
3) Total friend pairs are 435 - 90 = 345
For choosing committees, we have to choose to choose 3 pairs from 90 an then 3 pars from 345 such that each node of pairs is shared with another node. But how, can't get this.
Any other way to look at this problem?